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# Solutions for Chapter 2.1: Elementary Statistics: Picturing the World 5th Edition

## Full solutions for Elementary Statistics: Picturing the World | 5th Edition

ISBN: 9780321693624

Solutions for Chapter 2.1

Solutions for Chapter 2.1
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##### ISBN: 9780321693624

This textbook survival guide was created for the textbook: Elementary Statistics: Picturing the World, edition: 5. Since 40 problems in chapter 2.1 have been answered, more than 10301 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.1 includes 40 full step-by-step solutions. Elementary Statistics: Picturing the World was written by and is associated to the ISBN: 9780321693624.

Key Statistics Terms and definitions covered in this textbook
• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Discrete distribution

A probability distribution for a discrete random variable

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Event

A subset of a sample space.

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• False alarm

A signal from a control chart when no assignable causes are present

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• Geometric mean.

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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